When data from a table (or tables) needs to be manipulated, easier to deal with info in form of a matrix. Matrices FreshSophJunSen A0342 B0447 C2106 D1322 F1210

Terminology Entry: The individual pieces of data in the matrix are called entries. The entry in the i th row and j th column is: The diagonal entries occur when i = j. From previous matrix: Order: If a matrix has m rows and n columns, then the matrix has an order of

Special Matrices Identity: A square matrix with 1 for each diagonal entry and 0 for each non-diagonal entry. (written as I) Square: A matrix with m=n. Zero: A matrix with all entries = 0.

Special Matrices – continued Row: A matrix of order 1 by n, also called a row vector. Column: A matrix of order m by 1, also called a column vector.

Operations Multiply a matrix by a non-zero constant. Add two matrices of the same order. Subtract two matrices of the same order.

Balance of trade: A-B, exports - imports A: US oil and coal exports to Canada, Germany, and France B: US oil and coal imports from Canada, Germany, and France Example 1

Power to influence: in a flow of information, who is the key? Create two matrices, A and B, with the following entries: Example 2

Compute A+B. The row sum that is greatest in matrix A+B corresponds to person with most influence. Example 2 – continued